Tapered filter for alternating currents of varying frequency



' E. DlEl-rzEi TAPERED FILTER FORALTERNATING.'CURRENTS 0F VARYINGFREQUENCY l di g? VAVAVAV VAVVA'A p7 'fia/0' r www Filed Feb. 26, 192i1200 /a'oo 20.00 24.00 '25;20 ,Jada

Patented oct. i9, 192e.

D/IETZE, OF BROOKLYN,

EGINHARD TELEGRAPE COMPANY, A; CORPORATION .OF NEW YORK.

NEW YORK, .ASSIGNORA TO AMERICAN TELEPHONE TAPEEED FILTER non.AnTEnNnEINe-CUERENTS on vnnYmG FREQUENCY. i

Application led February By the term wave-filter I refer to a networkof'recurrent sections formed alike I -or according to some law ofprogressive change, and adapted freely to transmit currents offrequencies Within a certain range and to shunt out currents within adifferent frequency range. v The lprincipal object of my invention 1s toprovide sucha lter of taper1ng-charac teristic impedance; Anotherobjectfof my invention is to provide a filter adapted to be interposedwithout serious refiection loss or irregularit between lines orapparatus o f different c aracteristic impedance. Still anotherfobjectis to provide a filter of this type, all sections of which shall havethe same free transmission ranges land which shall have a definite andunvarying propa gation constant throughout its length.

In the following speciiication I have disclosed a limited number ofspecific embodiments of the invention, which I shall now proceed todescribe with the understanding that the definition of the invention 1sgiven j in the appended claims.

Referring to the drawings, Figure 1 is a diagram illustrating alter'embodying my invention. Fig. 2 is a diagram of a more specificexample. Fig. 3 is a diagram showing characteristic curves for the.filter of Fig. 2. Figs. 4 and `5 are diagrams show ing modifications.

is known how to make filters of recurrent sections, all alike, eachsection comprising series impedance 'or impedances and shunt impedanceor impedances. Fig. 1 can be looked upon as a filter of this type, pro.-vided the constant a appearing inthe legends is taken equal to 1. Withthis understanding, it will be, seen that the series impedances are eachal and the shunt impedances z2. The theory of such a iilter is commonly'developed on the assumption that there is an infinite number ofsections. The results obtained for the innite filter apply to a filterhaving only a initefnumber of sections, provided the proper terminalimpedance is employed.` The Yimpedancesz, and a, are made with as littledissipative loss as practicable, and vfor most purposes ac. 1921..seria11vo.`447,`a9s.

this loss can bev disregarded, and z, land a,

can be'lookedk upon as pure reactances.` The filter of Fig. 1 hasmid-series vtermination at the left, that is, 'the initialseries-impedance is 'only half that of the succeedingseries impedances.equal. 1 The foregoing discussion of Fig. 1 is on the express lassumtion that the constant a A1s equal to 1. y improvement involves makinga: different from 1. Assuming that the'first mid-series sectionextending A to B is as given in Fig. 1, I form the next mid-seriessection from B to C by multiplying each of the component impedanceelements by a. In the next section from C to D these elements aremultiplied by a2, and so on. This delines the structure of my `improvedfilter. mine the value to be given-to w will be diss cussed later.. Myimproved -ilter has the following properties:

definite and the same, no matter what value is given to a; accordinglythe 'same as for the non-tapered filter, corresponding to a=1.

2. The characteristic impedance from successive oints 0f junction of thesections is increase from section tosection by the factor ra, assuming a1, orV decreased in.

this ratio if a 1.

3. The propagation constant ris identical The shunt impedances are l.Its critical or cut-off frequencies are from The conditions that detelwfor all filter sections, both in the free trans-A mission and attenuated.frequency range.

I-Iaving the foregoing properties, it will be seen that my improvedfilter may be introduced between `two. lines or apparatus ofdiierentcharacteristic impedance, the Afilter beingdesigned so that itscharacteristic im- "pedance from section to section Ais graded betweenthe two extreme values of impedance. My tapered .filter then serves inall respects as an ordinary filter, and 'in addition it obviates the"disadvantage of large 4reflection loss that wouldl be had with anyordinary non-tapered lter; In the freev transmissionranges o'f a filterthe currents are displaced from section to section by a phase anglewhich varies from 0 at the one limit-in great extent these reflectionsannul one another. Perhaps this point may be made clearer by consideringthat the sum of a number of vectors of equal length and random directionwill be decidedly ess than if they all had the same direction.

That the characteristic impedance of my improved lter varies ingeometrical ratio from section to section with the factor a may he shownby the followinv Whatever the impedance i, at A, if each individualcomponent impedance element of the whole network be. multiplied by a,the resultant impedance will be aZo. But now considerations.

the filter viewed from A will be identical with what it was before whenlooking to the right from B, for itis assumed always that the filter hasan infinite number of sections. at B for thefilter as given in Fig. 1must be aZo. By similar reasoning it may be shown that at C thecharacteristic impedance must, be a2Z, and so on.

will ynow proceed to obtain a formula for vthe input characteristicimpedance Z0. From Kirchhoffs laws we 'get the equation The solution ofthis gives Knowing the impedance at vthe input end Z0, the lmpedance atany junction oint of the filter sections may be determine at once by theformula ZnIan--Zo where 71,:0 at the input end A, 1 at B, 2 at C, and soon.

That the propagation constant is the same at all points A, B, C, D,etc., may be shown as follows. By definition of the propagation constantI where the currents in the series elements of the successive nth and(n-l-l)th meshes are represented by In and IDH. Let the current intheintermediate shunt impedance element be I. Then we have the equationsInf n+1=I,n

and

I i n ana, Inn* allai anHZo) From thesetwo equations we obtain thesolution Thus the value of the current ratio in successive sections lofthe filter is seen to be independent of n, showing that P has the samevalue, whatever the value of n that is taken. This proves the constancyof theI propagation constant throughout the length ofthe filter.

In the ordinary filter to which the filter of Fig, 1 reduces when a=1,if We represent the propagation constant by F0, We have the a- 1 cosh1"=cosl1 PMI-0Wl smh I (7) and cosh 1"=cosh Io-l--q-l (8) From equations(7) and (8), the propagation constant of the tapered filter can easilybe compared with that of the non-tapered filter. In order to keepreflection effects b etween successive sections small, a value of ashould be taken differing only slightly from 1.

It will be seen that my improved filter involves making thecharacteristic impedance vary in geometrical ratiofrom section tosection. I have tried other laws ,for the progression of value of thecharacteristie impedance and I find that the law disclosed in thisspecification gives ap unique result.` Under other laws, a value ofthepropagation constant is obtained that can not be freed from fn., whichdefines the position of the section in the lter. 'l In Fig. 2 I haveillustrated a simple lowpass filter o f three sections designed for aspecific purpose and embodying thetapering construction heretoforedisclosed in this specification. The filter of Fig. l2 is intended tomake connection between a` low mpedance line of 600ohms and another lineHence the characteristic impedancel vas lis desired at a fre having animpedance of 2000 ohms. Thev critical or cut-off frequency of the filteris to be 2,500, and the maximum transmission uency of 800 cycles. Withthree sections t ere will be fourpoints of discontinuity: hence we havefor the determination of a, the equations Z0=600, @4Z :2,000, from whicha, is readily computed to be 1.35. I shall not take s acel here to givethe steps by which the va ues of e, and z2 are etermined as they arepractically the same non-tapered filter having the characteristicimpedance Z.I of the lter the two series impedances shown separately oneither side of a junction oint such as B in Fig. 1 will be consolidatedand inthe case of the low-pass filter of Fig. 2 their combination in asingle coil 1s shown. The resultant inductance values of the coilsappear as legends on Fig. 2. The' shunt impedances vary by `the factor a-.1.35; and accordingly the capacities of the condensers 2', 3 and C2vary inversely by the same factor. v

In Fig; 3 the heavy line shows, plotted against frequency, the currentreceived over the tapered filter per Avolt a plied at the sending end.The diagram-s ows how the filter cuts off at a frequencylof 2,500. Forcomparison Il have shown, in the light, continuous line,` thecorresponding characteristic that might be obtained witha nontaperedfilter inserted between two lines of equal im edance, thatis when thereare no reflection losses, and in the dotted line I have shown thecharacteristic for the nontapered filter vinserted between a G-ohm lineand a 200G-ohm line.v The number of sections in Fig. 2' is rather small;for a larger number of sections the transmission characteristic of thetapered filter would bev lim roved. i

e foregoing discussion is based on mid-series# geometrical law ofprogres'- sion is equally applicable for other sections and filtervterminations.

asin the case of the In the actual constructionv sections and filtertermination,y but the sameI Thus-alY lter may be terminated at:1J-series section and all the sections ma vbedivided accordingly. Thisis illustrate -in Fig. 4. It will be seen that the lter' of Fi.` 1 is aspecial case of Fig', 4, with w=i in ig; 1

Instead of .fr-series and mid-series sections one ma have -shuntsections. In this case a: times the shunt admittance is considered tobelong` to the section that follows and the remainder to the sectionthat precedes.' To make this clear on Fig. 5 the shunt im edances havebeen replaced bypairs of impedances with appropriate legends. By makingw=i, we special case of mid-shunt sections and termination.

1. The method of reducing the total reflection loss in a sectionalalternating current filter between lines or apparatus of differentcharacteristic impedance, which consists in partially reflecting thecurrents' at eachl successive section of the "filter, whereby' thevector sum of the partial reflections will be less than the totalreflection would be if the impedance irregularity were all at one place.

2. The method of reducing yreilection losses in Ia filter Ainterposedbetween `lines Nor apparatus of different characteristic impedance,which consists in dividin up the reflection at different points iniferent phase throughout the filter, and thereby largely neutralizingthe reflection effects.

3. n the operatlon of a filter of recurrent section type, the method ofltering alternating currents of a certain frequency rangefrom a circuitof'one impedance value to a circuit of another impedance value, which'consists in producing partial reflection effects at the respectivesections due to ave the corresponding differences of limpedance betweenthem.

In testimony whereof. I have signed myA name to this specification.this'18th day of February, 1921.

EGINHABD DIETZE.

